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Let X₁,..., Xn,... ~ iid Beta(0, 1). (a) Using the CLT and the Delta Method, find an asymptotic distribution relating to the MOM estimator for 0. Gy

Let X₁,..., Xn,... ~ iid Beta(0, 1). (a) Using the CLT and the Delta Method, find an asymptotic distribution relating to the MOM estimator for 0. Gy

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Let X₁,..., Xn,... ~ iid Beta(0, 1). (a) Using the CLT and the Delta Method, find an asymptotic distribution relating to the MOM estimator for 0. (b) Provide a asymptotic distribution relating to the MLE Ôn = n/1 log(X₂). (c) Compare the asymptotic variances of these two estimators to make a determination about which is better (lower variance) in the long run. Is this result expected?
Transcribed Image Text:Let X₁,..., Xn,... ~ iid Beta(0, 1). (a) Using the CLT and the Delta Method, find an asymptotic distribution relating to the MOM estimator for 0. (b) Provide a asymptotic distribution relating to the MLE Ôn = n/1 log(X₂). (c) Compare the asymptotic variances of these two estimators to make a determination about which is better (lower variance) in the long run. Is this result expected?
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